A right triangle is shown which equation could be used to find the value for a
1 answer:
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The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is
and
We have given that,
f(x) = 2x^2 + x + 4
x g(x)
-2 1
-1 3
0 5
1 7
2 9
<h3>What is a polynomial function?</h3>A polynomial function is a relation where a dependent variable is equal to a polynomial expression.
A polynomial expression is an expression including numbers and variables, where variables are raised to non-negative powers.
The general form of a polynomial expression is:
a₀ + a₁x + a₂x² + a₃x³ + ... + anxⁿ.
The highest power to a variable is the degree of the polynomial expression. When degree = 2, the function is a quadratic function.
When degree = 1, the function is a linear function.
<h3>How do we solve the given question?</h3>
The quadratic function is given to us:f(x) = 2x^2 + x + 4.
We need to determine the linear equation g(x).
Since it's a linear equation we use the two-point method to determine the equation.
<h3>What is the two-point?</h3>y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)
We take the points g(-2) =1, g(-1) = 3
g(x) - g(1) = ((g(-2)-g(-1))/(-2+1))*(x-1)or,
g(x) - 1 = ((-2-(-1))/(-2+1))*(x-1)or, g(x) - 1 = -1(-x+1)or,
g(x) = x - 1 + 1 = x
∴ g(x) = x , is the linear function g(x)
We are asked to find the solution to the system of equations f(x) and g(x).To find the solution we need to check what is the common solution to both f(x) and g(x).
For that, we equate f(x) and g(x).2x^2 + x + 4 = x or, 2x² - x +x- 4 = 0or, 2x^2 - 4 = 02(x^2-2)=0x^2-2=0g(-1) = 3(from the table)
The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is and
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Answer:
The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three is
Step-by-step explanation:
Given : Fred flips a coin, spins the spinner, and rolls a standard number cube.
To find : The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three ?
Solution :
First we find probability one by one,
1) Flips a coin - Head, Tail
Total number of outcome = 2
Favorable outcome (getting a tail) = 1
Probability that the coin will show tails is
2) Spins the spinner - yellow, green, blue
Total number of outcome = 3
Favorable outcome (land on yellow or green) = 2
Probability that the spinner will land on yellow or green
3) Rolls a standard number cube - 1,2,3,4,5,6
Total number of outcome = 6
Favorable outcome (show a three) = 1
Probability that the cube will show a three
The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three is
Therefore, The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three is